^{1}

^{1}

^{1}

^{1}

A reliable approach based on modified facet-based model and Vector Radiative Transfer theory is presented to calculate electromagnetic scattering from a particular electrically large sea surface superimposed with foams, which can handily give both monostatic and bistatic scattering results and could be applied to synthetic aperture radar imagery simulation. The facet model is derived from Fuks’ first-order small perturbation method function, and then the Kirchhoff model is introduced to revise the results in view of the dependency on cut-off wave number at near vertical incidence angles. Additionally, the contributions of foams are taken into consideration on the basis of Vector Radiative Transfer theory. The accuracy and superiority of this proposed approach are demonstrated in comparison with traditional facet model, which illustrates that the results of this approach agree better with experimental results. Moreover, several examples are given to verify that the proposed approach is of more significance at large incidence angles and high wind speed.

Investigation on electromagnetic (EM) scattering from maritime scene is of great value in both civil and military applications, such as maritime environment monitoring and clutter rejection in target detection. Extensive endeavors have been devoted to evaluate the scattering characteristic in either theoretical or experimental terms. Usually, approaches for EM scattering calculation from rough sea surface in theoretical term can be classified as numerical category and analytical category. Among the numerical efforts, some recent attempts could be noted, for instance, the Multiple Sweep Method of Moments [

In past decades, synthetic aperture radar (SAR) has been greatly developed in consideration of its independency on daylight and weather, and SAR imaging has become one of the most important means for remote sensing of maritime environment. At the same time, local information is useful and desirable in SAR imagery simulation of marine scene, especially the one with oil film and ship wake. This demand has encouraged the development of facet-based approaches, which try to break the surface into facets and then the scattering contributions from individual facets could be obtained. A facet backscattering model was presented by Franceschetti et al. by means of Kirchhoff approximation [

In reality, with the increase of wind speed above sea surface, foams would come into being. What is more, one-third of sea surface would be covered with foams when the velocity of wind comes up to 25 m/s. So it is of great significance to take the influences of foams on sea surface scattering into account at high wind speed condition. Jin [

In this work, a facet-based model derived from Fuks’ first-order small perturbation method function [

Sea surface can be seen as a two-scale model where small-scale waves are superimposed on the large-scale waves. The ELH spectrum [

As shown in Figure

Geometry of microscopic rough scattering surface.

Next, we need to calculate the scattering coefficient of arbitrary slope facet.

As shown in Figure

Geometry of global coordinate and local coordinate.

Referring to (

According to the Bragg resonance hypothesis, both the Bragg waves spreading along and against the radar sight direction contribute to the radar receiver; thus (

Thus, cut-off wave number

Assume that the lengths of the two-dimensional simulation sea surface sample in

Unfortunately, there is no unified standard to choose the advisable cut-off wave number. As shown in Figure

Impact of cut-off wave number on scattering coefficients.

The parameters in the simulation are in order as follows: the incident wave is at Ku-band (14.0 GHz), the wind speed at 10 m above the mean sea level is selected by

In view of the dependency on cut-off wave number at near vertical incident angles, Kirchhoff model can be introduced to revise the slope-modulated perturbation coefficient [

By now, we can calculate the total scattering coefficient of a particular sea surface sample by (

In reality, with the increase of wind speed above the sea surface, foams come into being. So it is inaccurate to calculate the scattering from sea surface with forenamed modified facet-based model and the influences of foams on sea surface scattering should be taken into account at high-wind-speed condition.

As shown in Figure

Geometry of foams scattering.

The bistatic scattering coefficient of sea surface with foams can be defined as [

We can further get the zeroth-order and first-order scattering coefficients

Scattering processes of different coefficients.

In consequence, the scattering coefficient of the area covered with foams can be calculated by

In fact, it could be assumed that the foams are made up of many water-air particles which could be represented by the model in Figure

Geometry of foams.

The coverage percentage of foams in wind-driven sea surface is intimately related to wind speed and seawater temperature. While the temperature difference between air and seawater is moderate, it can be calculated by

Then the number of facets covered with foams is

As a result, we can calculate the total scattering coefficient of a particular wind-driven sea surface covered with foams by

The accuracy and validity of the scheme proposed in this paper are verified by comparing the backward-scattering results of the presented approach with those of traditional facet model and experimental results in [

Comparison of backward-scattering results between and among the presented approach, traditional facet model, and experiment. (a) HH polarization. (b) VV polarization.

For further validation, Figure

Comparison of backward-scattering results at different wind speeds.

In order to investigate the impact of azimuth angles on backward-scattering coefficients, the results at different azimuth angles are demonstrated in Figure

Impact of azimuth angles on backward-scattering coefficients.

In this paper, a reliable approach based on MFBM and VRT theory is developed for the calculation of scattering from a particular electrically large sea surface covered with foams. This proposed scheme is of more comprehensive significance because the contributions from not only the specular and diffuse configurations but also the foams are taken into consideration. Moreover, it can handily give both the monostatic and bistatic scattering results and could overwhelm the application to SAR imagery simulation. The comparisons show better agreement with experimental results than traditional facet model, which demonstrates the accuracy and superiority of this scheme. Additionally, numerical results show that the contributions of foams are assignable and of great significance at large incidence angles and high wind speeds.

The polarization factor

The polarization factor

The authors declare that there are no conflicts of interest regarding the publication of this paper.

This work was supported by National Natural Science Foundation of China under Grant no. 61372033.